I have some confusion over some diagrams involved in proton decays in SU(5). I've seen a few like this that look weird to me. Here is one I found where the colored Higgs triplet does the job:(adsbygoogle = window.adsbygoogle || []).push({});

Straight away I don't know what to make of this because I've only ever seen diagrams where fermions are connected by one exchange boson. Here there are two, the [itex]T[/itex] and [itex]\overline{T}[/itex].

If I'm not mistaken, [itex]T[/itex] is meant to have a charge of -1/3 and [itex]\overline{T}[/itex] has +1/3. So if I specify the left hand side quarks with two of the three (uud) proton constituents, [itex]u^{+2/3}[/itex] and [itex]d^{-1/3}[/itex], then the charge from those quarks going into the left vertex is +1/3 overall. So there should be a [itex]\overline{T}[/itex] coming out of that vertex since it also has charge +1/3. But then the arrows look wrong since the arrows on the u, d should be pointing to the right?

Anyway, then the right hand side vertex would have [itex]\overline{T}[/itex] going in, so then the leading decay mode in this situation ([itex]p \rightarrow K^{+} \overline{\nu}[/itex]) would invove the Q on the right hand side being an [itex]\overline{s}[/itex] with charge of +1/3 (with the spectator u quark (which isn't shown) combining with the [itex]\overline{s}[/itex] to produce the [itex]K^{+}[/itex]), and the antilepton L being neutral, ie. [itex]\overline{\nu}[/itex].

So the diagram seems to make sense if I ignore one of the bosons. Has whoever drew this diagram combined two different interactions into the same diagram here, and if so, do the arrows really make sense? Or am I misinterpreting the [itex]T[/itex] / [itex]\overline{T}[/itex] line in this diagram?

Here's another one, this time a SUSY diagram:

The [itex]u^{+2/3}[/itex] and [itex]d^{-1/3}[/itex] put an overall +1/3 charge into the red dot vertex, the anti-stop (anti based on the arrow direction) has a -2/3 charge and the anti-stau a +1 charge, so the red dot vertex has overall +1/3 coming out of it too. So far so good.

Then we get to the vertices with the Higgsino. At the upper vertex, there's a -2/3 charge going in from the stop, and the anti-strange quark has charge +1/3, so the Higgsino must be a -1 charge (ie. it must be the anti-particle of the superpartner to the [itex]H^{+}[/itex] in the [itex](H^{+}, H^{0})[/itex] SU(2) doublet within the SU(5) [itex]\psi_{\textbf{5}}[/itex] multiplet). Similarly the +1 of the anti-stau and the -1 of the anti-Higgsino cancel to give the electrically neutral antineutrino.

--> Assuming the above interpretation is correct, my issues with this are:

1) Is there a reason why this diagram, meant to indicate proton decay, is set up to be read left-to-right rather than right-to-left?

2) I believe this decay is described by what gets referred to as a 'dimension 5' operator. I think that refers to what is happening at the red dot. However, I don't understand the '5' part. There are only 4 fields involved [itex](u, d, \tilde{t},\tilde{\tau})[/itex]. What is '5-dimensional' about this situation?

**Physics Forums - The Fusion of Science and Community**

Dismiss Notice

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Confused by these proton decay diagrams

Loading...

Similar Threads - Confused proton decay | Date |
---|---|

B Proton emission equation | Jan 22, 2018 |

A Confusion regarding the $\partial_{\mu}$ operator | Jul 24, 2017 |

I Confused about Feynman diagrams | Jul 16, 2017 |

Confusion with the Gordon identity | Feb 17, 2016 |

Confused about isospin conservation in rho to pion decays | Jul 31, 2015 |

**Physics Forums - The Fusion of Science and Community**